Preheat oven to 325 degrees Fahrenheit. Spray a 9x13-inch baking dish with Pam, line with parchment paper & spray with Pam again. Set aside.
Cut pandesal into 1-inch pieces and place them on a sheet pan lined with a silicone mat.
Bake, tossing halfway through until pieces are very dry and slightly toasted, 15-25 minutes. Let cool, then transfer to the prepared 9x13-inch baking dish.
In a large bowl, whisk eggs, granulated sugar, and salt until lightened, about 30 seconds; set aside.
In a medium saucepan, whisk brown sugar with cocoa to combine. Whisk in milk and cream and heat over medium heat until warm. Mix in bittersweet chocolate and instant coffee until chocolate is melted. Pour some of the mixture into the large bowl with eggs to temper the custard in a thin stream.
Whisk the rest of the chocolate mixture into the egg mixture until combined. Whisk in vanilla extract.
Add the chocolate custard mixture to the 9x13 pan and gently toss the bread cubes to evenly moisten the bread. Let the mixture sit to allow bread to thoroughly saturate, 30 to 45 minutes, occasionally pressing bread gently with rubber spatula. Adjust oven rack to middle position and preheat oven to 325 degrees F.
Tuck chopped semisweet chocolate into bread pudding, evenly distributing. Bake until pudding is just set in center, 45 to 55 minutes. Remove from oven and let cool about 30 minutes before serving.
Top with a drizzle of chocolate ganache and tiny marshmallows. Store leftovers in the refrigerator.